Extends the class ContinuousDistribution for the uniform distribution [96] (page 276) over the interval. More...

Inheritance diagram for umontreal.ssj.probdist.UniformDist:

Public Member Functions
	UniformDist ()
	Constructs a uniform distribution over the interval \((a,b) = (0,1)\).
	UniformDist (double a, double b)
	Constructs a uniform distribution over the interval \((a,b)\).
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
double	getA ()
	Returns the parameter \(a\).
double	getB ()
	Returns the parameter \(b\).
void	setParams (double a, double b)
	Sets the parameters \(a\) and \(b\) for this object.
double[]	getParams ()
	Return a table containing the parameters of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

Static Public Member Functions
static double	density (double a, double b, double x)
	Computes the uniform density function \(f(x)\) in ( `funiform` ).
static double	cdf (double a, double b, double x)
	Computes the uniform distribution function as in ( `cdfuniform` ).
static double	barF (double a, double b, double x)
	Computes the uniform complementary distribution function.
static double	inverseF (double a, double b, double u)
	Computes the inverse of the uniform distribution function ( `cdinvfuniform` ).
static double[]	getMLE (double[] x, int n)
	Estimates the parameter \((a, b)\) of the uniform distribution using the maximum likelihood method, from the \(n\) observations.
static UniformDist	getInstanceFromMLE (double[] x, int n)
	Creates a new instance of a uniform distribution with parameters.
static double	getMean (double a, double b)
	Computes and returns the mean \(E[X] = (a + b)/2\) of the uniform distribution with parameters \(a\) and \(b\).
static double	getVariance (double a, double b)
	Computes and returns the variance \(\mbox{Var}[X] = (b - a)^2/12\) of the uniform distribution with parameters \(a\) and \(b\).
static double	getStandardDeviation (double a, double b)
	Computes and returns the standard deviation of the uniform distribution with parameters \(a\) and \(b\).

Detailed Description

Extends the class ContinuousDistribution for the uniform distribution [96] (page 276) over the interval.

\([a,b]\). Its density is

\[ f(x) = 1/(b-a) \qquad\mbox{ for } a\le x\le b \tag{funiform} \]

and 0 elsewhere. The distribution function is

\[ F(x) = (x-a)/(b-a) \qquad\mbox{ for } a\le x\le b \tag{cdfuniform} \]

and its inverse is

\[ F^{-1}(u) = a + (b - a)u \qquad\mbox{for }0 \le u \le1. \tag{cdinvfuniform} \]

Definition at line 44 of file UniformDist.java.

Constructor & Destructor Documentation

◆ UniformDist() [1/2]

umontreal.ssj.probdist.UniformDist.UniformDist ( )

Constructs a uniform distribution over the interval \((a,b) = (0,1)\).

Definition at line 51 of file UniformDist.java.

◆ UniformDist() [2/2]

umontreal.ssj.probdist.UniformDist.UniformDist	(	double	a,
		double	b )

Constructs a uniform distribution over the interval \((a,b)\).

Definition at line 58 of file UniformDist.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.UniformDist.barF	(	double	a,
		double	b,
		double	x )

static

Computes the uniform complementary distribution function.

\(\bar{F}(x)\).

Definition at line 121 of file UniformDist.java.

◆ barF() [2/2]

double umontreal.ssj.probdist.UniformDist.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 70 of file UniformDist.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.UniformDist.cdf	(	double	a,
		double	b,
		double	x )

static

Computes the uniform distribution function as in ( cdfuniform ).

Definition at line 106 of file UniformDist.java.

◆ cdf() [2/2]

double umontreal.ssj.probdist.UniformDist.cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements umontreal.ssj.probdist.Distribution.

Definition at line 66 of file UniformDist.java.

◆ density() [1/2]

double umontreal.ssj.probdist.UniformDist.density	(	double	a,
		double	b,
		double	x )

static

Computes the uniform density function \(f(x)\) in ( funiform ).

Definition at line 94 of file UniformDist.java.

◆ density() [2/2]

double umontreal.ssj.probdist.UniformDist.density ( double x )

Returns \(f(x)\), the density evaluated at \(x\).

Parameters

x	value at which the density is evaluated

Returns: density function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 62 of file UniformDist.java.

◆ getA()

double umontreal.ssj.probdist.UniformDist.getA ( )

Returns the parameter \(a\).

Definition at line 233 of file UniformDist.java.

◆ getB()

double umontreal.ssj.probdist.UniformDist.getB ( )

Returns the parameter \(b\).

Definition at line 240 of file UniformDist.java.

◆ getInstanceFromMLE()

UniformDist umontreal.ssj.probdist.UniformDist.getInstanceFromMLE	(	double[]	x,
		int	n )

static

Creates a new instance of a uniform distribution with parameters.

\(a\) and \(b\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\).

Parameters

x	the list of observations to use to evaluate parameters
n	the number of observations to use to evaluate parameters

Definition at line 188 of file UniformDist.java.

◆ getMean() [1/2]

double umontreal.ssj.probdist.UniformDist.getMean ( )

Returns the mean.

Returns: the mean

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 78 of file UniformDist.java.

◆ getMean() [2/2]

double umontreal.ssj.probdist.UniformDist.getMean	(	double	a,
		double	b )

static

Computes and returns the mean \(E[X] = (a + b)/2\) of the uniform distribution with parameters \(a\) and \(b\).

Returns: the mean of the uniform distribution \(E[X] = (a + b) / 2\)

Definition at line 199 of file UniformDist.java.

◆ getMLE()

double[] umontreal.ssj.probdist.UniformDist.getMLE	(	double[]	x,
		int	n )

static

Estimates the parameter \((a, b)\) of the uniform distribution using the maximum likelihood method, from the \(n\) observations.

\(x[i]\), \(i = 0, 1, …, n-1\). The estimates are returned in a two-element array, in regular order: [ \(a\), \(b\)]. The maximum likelihood estimators are the values \((\hat{a}\), \(\hat{b})\) that satisfy the equations

\begin{align*} \hat{a} & = \min_i \{x_i\} \\ \hat{b} & = \max_i \{x_i\}. \end{align*}

See [114] (page 300).

Parameters

x	the list of observations used to evaluate parameters
n	the number of observations used to evaluate parameters

Returns: returns the parameters [ \(\hat{a}\), \(\hat{b}\)]

Definition at line 163 of file UniformDist.java.

◆ getParams()

double[] umontreal.ssj.probdist.UniformDist.getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in regular order: [ \(a\), \(b\)].

Implements umontreal.ssj.probdist.Distribution.

Definition at line 260 of file UniformDist.java.

◆ getStandardDeviation() [1/2]

double umontreal.ssj.probdist.UniformDist.getStandardDeviation ( )

Returns the standard deviation.

Returns: the standard deviation

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 86 of file UniformDist.java.

◆ getStandardDeviation() [2/2]

double umontreal.ssj.probdist.UniformDist.getStandardDeviation	(	double	a,
		double	b )

static

Computes and returns the standard deviation of the uniform distribution with parameters \(a\) and \(b\).

Returns: the standard deviation of the uniform distribution

Definition at line 226 of file UniformDist.java.

◆ getVariance() [1/2]

double umontreal.ssj.probdist.UniformDist.getVariance ( )

Returns the variance.

Returns: the variance

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 82 of file UniformDist.java.

◆ getVariance() [2/2]

double umontreal.ssj.probdist.UniformDist.getVariance	(	double	a,
		double	b )

static

Computes and returns the variance \(\mbox{Var}[X] = (b - a)^2/12\) of the uniform distribution with parameters \(a\) and \(b\).

Returns: the variance of the uniform distribution \(\mbox{Var}[X] = (b - a)^2 / 12\)

Definition at line 213 of file UniformDist.java.

◆ inverseF() [1/2]

double umontreal.ssj.probdist.UniformDist.inverseF	(	double	a,
		double	b,
		double	u )

static

Computes the inverse of the uniform distribution function ( cdinvfuniform ).

Definition at line 135 of file UniformDist.java.

◆ inverseF() [2/2]

double umontreal.ssj.probdist.UniformDist.inverseF ( double u )

Returns the inverse distribution function \(x = F^{-1}(u)\).

Restrictions: \(u \in[0,1]\).

Parameters

u	value at which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Exceptions

IllegalArgumentException if \(u\) is not in the interval \([0,1]\)

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 74 of file UniformDist.java.

◆ setParams()

void umontreal.ssj.probdist.UniformDist.setParams	(	double	a,
		double	b )

Sets the parameters \(a\) and \(b\) for this object.

Definition at line 247 of file UniformDist.java.

◆ toString()

String umontreal.ssj.probdist.UniformDist.toString ( )

Returns a String containing information about the current distribution.

Definition at line 268 of file UniformDist.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/probdist/UniformDist.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ UniformDist() [1/2]

◆ UniformDist() [2/2]

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ density() [1/2]

◆ density() [2/2]

◆ getA()

◆ getB()

◆ getInstanceFromMLE()

◆ getMean() [1/2]

◆ getMean() [2/2]

◆ getMLE()

◆ getParams()

◆ getStandardDeviation() [1/2]

◆ getStandardDeviation() [2/2]

◆ getVariance() [1/2]

◆ getVariance() [2/2]

◆ inverseF() [1/2]

◆ inverseF() [2/2]

◆ setParams()

◆ toString()